i must say i am nor a 737 neither a 737 driver but this all sounds strange.
here is a good description of flexing and derating on example 737
A temporary form of de-rating known as a "T/O de-rate" is accessible through the FMC on TAKEOFF REF 2/2 or N1 LIMIT (NG's) but this is prohibited by some operators. The T/O de-rates (TO-1 & TO-2) can be 10 to 20%. It follows that an engine may be de-rated and also be using reduced thrust in which case you could be taking off at Full power -20% -25% = 60% of the full power of the engine - scary thought! Note that a T/O de-rate can overridden by firewalling the thrust levers; this action will give the thrust rating shown on the IDENT page.
from b737.org.uk
you have to consider if the thrust was derated by a technican on ground ( i.e mixing two different rated engines) or by pilot via fms.
in the first case the "full" rated thrust is not available by pilot action since its a permanent derating ( e.g the 737NG can be supplied by 22K 24K 26K etc engines which are basicly the same but with different max power settings)
the second scenario is a derating via fms by the pilot- and here in every me known airplane disengaging autothrust and firewalling the levers will give maximum certified thrust of the engine cancelling any thrust reductions that had been set for a reduced takeoff.
i cannot imagine on a 777 you cannot cancel a pilot chosen TO derated thrust by firewalling.
you also have to consider if its a fadec controlled engine or not. fadec will give you always the "only" maximum of the engine without exeeding limits.
at non fadec planes you of course have to be very careful with simply firewalling.
at the bae146 i have flown there is a thrust modulation system in which you set a flex n1 by tables.
you have simulatan a bug on the n1 gauge where the n1ref- the maximum allowable for the temperature and elevation is shown. in every case simply pushing the levers forward will give you the un-derated thrust ( bae146)
firewalling on the bae146 may toast the engines, you will exeed EGT limits.
there was due to the OM one exeption : wind shear.
there was written that at a windshear where even at full rated thrust and stickshaker activated the plane has negative rate of climb and ground contact is likely push the power levers full forward regardless of EGT redline.
after doing this return to max continus as soon as possible , land as soon as possible and all engines has to be removed and inspected before next flight.